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schur(List,AbstractSheaf) -- apply a Schur functor to an abstract sheaf

Synopsis

Function: schur
Usage:

schur(p,E)

schur_p E
Inputs:
- p, a partition, specified by a descending list of non-negative integers
- E,
Outputs:
- the result of applying the Schur functor corresponding to the partition $p$ to $E$

Description

i1 : base(3, Bundle => (E,3,c))

o1 = a variety

o1 : an abstract variety of dimension 3

i2 : chern E

o2 = 1 + c  + c  + c
          1    2    3

o2 : QQ[c ..c ]
         1   3

i3 : chern schur_{1,1,1} E

o3 = 1 + c
          1

o3 : QQ[c ..c ]
         1   3

i4 : chern schur_{2,1} E

                   2              3
o4 = 1 + 8c  + (26c  + 6c ) + (44c  + 36c c )
           1       1     2        1      1 2

o4 : QQ[c ..c ]
         1   3

i5 : chern schur_{3} E

                    2               3
o5 = 1 + 10c  + (40c  + 15c ) + (82c  + 111c c  + 27c )
            1       1      2        1       1 2      3

o5 : QQ[c ..c ]
         1   3

See also

exteriorPower(ZZ,AbstractSheaf)
symmetricPower(RingElement,AbstractSheaf) -- symmetric power of an abstract sheaf

Ways to use this method:

schur(List,AbstractSheaf) -- apply a Schur functor to an abstract sheaf